Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929651052445696 |
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| author | Affonso, Lucas Bissacot, Rodrigo Corsini, Henrique Welsch, Kelvyn |
| author_facet | Affonso, Lucas Bissacot, Rodrigo Corsini, Henrique Welsch, Kelvyn |
| contents | Following seminal work by J. Fröhlich and T. Spencer on the critical exponent $α=2$, we give a proof via contours of phase transition in the one-dimensional long-range ferromagnetic Ising model in the entire region of decay, where phase transition is known to occur, i.e., polynomial decay $α\in (1,2]$. No assumptions that the nearest-neighbor interaction $J(1)$ is large are made. The robustness of the method also yields a proof of phase transition in the presence of a nonsummable external field that decays sufficiently fast. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours Affonso, Lucas Bissacot, Rodrigo Corsini, Henrique Welsch, Kelvyn Mathematical Physics Statistical Mechanics Probability 82B05, 82B26, 82B20, 82Bxx Following seminal work by J. Fröhlich and T. Spencer on the critical exponent $α=2$, we give a proof via contours of phase transition in the one-dimensional long-range ferromagnetic Ising model in the entire region of decay, where phase transition is known to occur, i.e., polynomial decay $α\in (1,2]$. No assumptions that the nearest-neighbor interaction $J(1)$ is large are made. The robustness of the method also yields a proof of phase transition in the presence of a nonsummable external field that decays sufficiently fast. |
| title | Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours |
| topic | Mathematical Physics Statistical Mechanics Probability 82B05, 82B26, 82B20, 82Bxx |
| url | https://arxiv.org/abs/2412.07098 |